12C Maths – Semester 1
Structures and Patterns
Vectors and Applications
Calculus I
Matrices and Applications
Calculus II
1
UNIT LEARNING GOALS:

recognition of patterns in well-known structures including Pascal's Triangle
and Fibonacci sequence

applications of patterns

use of the method of finite differences

proof by induction

use mathematical induction to prove de Moivre’s Theorem
---------------------------------------------------------------------------------
scalar product of two vectors

vector product of two vectors

unit vectors

resolution of vectors into components acting at right angles to each other

calculation of the angle between two vectors

applications of vectors in both life-related and purely mathematical
situations
---------------------------------------------------------------------------------------
development and use of Simpson’s rule
 approximating small changes in functions using derivatives
-------------------------------------------------------------------------------------
applications of matrices in both life-related and purely mathematical
situations
 relationship between matrices and vectors
----------------------------------------------------------------------------------
integrals of the form

simple integration by parts

solution of simple, linear, first order differential equations with constant
coefficients
12C Maths – SEMESTER 2
Assessment

Exam each term

Assignment each term
Success Criteria:

Accurate and successful
completion of problems from the
textbook.

Reached set Target.
Key Verbs
 Understand
 Manipulation
 Calculate
 Resolve
 Integrate
Resources
Q MATHS 12C
Real and Complex Number Systems
Calculus III
Dynamics
Linear Programming
1
UNIT LEARNING GOALS:
-------------------------------------------------------------------------------
use of complex numbers in proving trigonometric identities

powers of complex numbers including de Moivre’s Theorem
 simple, purely mathematical applications of complex numbers
-------------------------------------------------------------------------------------------
life-related applications of simple, linear, first order differential
equations with constant coefficients
-------------------------------------------------------------------------------
application of derivatives and integrals and Newton’s laws of motion
in vector form to:
straight line motion in a horizontal plane with variable force
vertical motion under gravity with and without air resistance
projectile motion without air resistance
simple harmonic motion (derivation of the solutions to differential equations
is not required)
circular motion with uniform angular velocity
-------------------------------------------------------------------------------------------------
recognition that the region bounded by the constraints gives the
feasible (possible) solutions

recognition that different values of the objective function in two
variables can be represented by a series of parallel lines

use of a series of parallel lines to find the optimal value of the
objective function in two variables (parallel or rolling ruler, graphical
method)

observation that the feasible region is always convex, and thus the
optimal solutions occur at an edge or a corner point of the feasible
region

interpretation of mathematical solutions and their communication in a
form appropriate to the given problem

relationship between algebraic and geometric aspects of problems
with constraints in two and three dimensions

use of the simplex algorithm to solve life-related problems in which
maximal solutions are required, and all constraints place positive,
upper bounds on the variables.
Assessment

Exam
Success Criteria:

Accurate and successful completion of
problems from the textbook.

Reached set Target
Key Verbs




Resources
Define
Calculate
Solve
Apply
Q Maths 12C